Pressure, Temperature, and Wind in the Atmosphere. 21 



According to the results of the discussion in the following 

 paper, the phase of the diurnal pressure -wave ought to 

 exceed that of the temperature-wave by an angle between 

 90° and 180° ; while the corresponding difference for the 

 semi-diurnal waves is 90°, agreeing closely with the observed 

 difference. 



This difference of phase arises from the change in the 

 pressure-wave with altitude, a change neglected when the 

 atmosphere is treated as a thin shell. The motion of the air 

 in the pressure-wave is very different from what it would be 

 if the pressure distribution were steady or changed slowly. 

 In a recent paper by Professor Hann *, on the daily variation 

 of wind force on mountain peaks in South India, he applies 



the formula v= — : — ; 7- metres/sec. to obtain an estimate 



sm 9 



of the semi-diurnal variation in wind velocity from the 

 pressure distribution, by taking for AB the mean gradient 

 from trough to crest in the pressure-wave. Now the formula 

 used applies only if the motion is steady and perpendicular 

 to the gradient, and it cannot be assumed that these con- 

 ditions are fulfilled in the case of the semi-diurnal variation 

 of wind. In fact, as the following investigation shows, the 

 wind is at some parts of the pressure-wave along the gradient, 

 while at others it is perpendicular to it as in ordinary steady 

 motion. 



I. 



If the effect of the Earth's rotation and the vertical motion 

 are neglected, the equations for the motion associated with a 

 pressure variation given by 



jp=^ [l + E 1 sin(ni+X 1 )+E 3 sin {2nt + 2\ 2 ) 

 are 



d 2 % _ dp d 2 rj _ dp 



P aW~~cLv' P dt 2 ~~Ty' 



where the axes of x and y are E. and S. and f, n are the 

 displacements of air originally at (x, y). 1£ <f> is north polar 

 distance and A east longitude 



dp 1 dp dp 1 dp 



dx ~ R sin (j> dX ' dy ~~ R d(f> ' 



where R is the Earth's radius. Therefore if E x E 2 are 



* Sitzunqsberichte der AJcad. der Jl'issenschaften in Wien, 1908 ; Met. 

 Zeit. p. 220 (1908). 



